Problem: Multiply the following complex numbers: $({5+5i}) \cdot ({-5-i})$
Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({5+5i}) \cdot ({-5-i}) = $ $ ({5} \cdot {-5}) + ({5} \cdot {-1}i) + ({5}i \cdot {-5}) + ({5}i \cdot {-1}i) $ Then simplify the terms: $ (-25) + (-5i) + (-25i) + (-5 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -25 + (-5 - 25)i - 5i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -25 + (-5 - 25)i - (-5) $ The result is simplified: $ (-25 + 5) + (-30i) = -20-30i $